In the characterization of oil fields in the petroleum industry, three-dimensional (3D) modeling using geostatistics is often used to assess reservoir heterogeneity and connectivity. Geostatistics often uses kriging to interpolate between data points or conditioning data. Conditioning data includes well log hard data, but can also include soft data, typically seismic data.
Conventional 3D modeling methods are based on variogram or two-point-statistics. Variogram-based algorithms allow integrating well and seismic data using a pixel-based approach. First, well data are blocked to the reservoir stratigraphic grid, i.e. well data values are assigned to the cells that the wells penetrate and sample. Then, all unsampled cells in the reservoir stratigraphic grid are simulated conditional to well and seismic data using some form of kriging. However, the models built using conventional variogram-based methods are most often not consistent with geological interpretation. Variogram-based geostatistics is inadequate in integrating geological concepts: two-point statistics variograms do not allow modeling complex geological heterogeneity. As a result, the variogram-based methods usually generate models that provide poor reservoir performance forecasting.
Over the past 10 years, the traditional variogram-based methods have been replaced by Multiple Point Statistics (MPS) methods. The MPS approach replaces traditional variograms with 3D numerical conceptual models of the subsurface geology, also known as training images.
MPS simulation is a reservoir facies modeling technique that uses conceptual geological models as 3D training images (or training cubes) to generate geologically realistic reservoir models. The training images provide a conceptual description of the subsurface geological geobodies, based on well log interpretation and general experience in reservoir architecture modeling. MPS simulation extracts multiple-point patterns from the training image and anchors the patterns to reservoir well data. A 3D data template is provided by a user to define the dimensions of the multi-point patterns to be reproduced from the training image. Specifically, a size of the 3D data template corresponds to the maximum number of conditioning data used to infer statistics from the training image during the MPS simulation process.
Another facies modeling technique is the object-based modeling (also referred to as Boolean modeling) technique. Object-based modeling is a method that uses and distributes quantifiable 3D facies geometries or shapes in an earth model. In the object-based modeling method, a variety of predefines 3D geological shapes, such as polygonal shapes, cylindrical shapes or more complex shapes, are used to model distribution of facies in an earth model.
Both multi-point statistics (MPS) and object-based modeling have advanced the state-of-the-art in geostatistical facies-based property modeling to build geocellular models for reservoir simulation. MPS has the benefit that it can far more easily match conditioning facies data with well data. Object-based modeling has the benefit that “depositional” property trends (such as sedimentary deposits) can be placed within the objects that follow the boundaries of the objects in a way that resembles true sedimentary deposits.
However, none of the conventional methods achieves the desired result in creating a facies-based reservoir model that can match conditioning facies data with well data as well as provide the ability to place depositional trends within boundaries of objects to simulate true sedimentary deposits. Furthermore, none of the conventional methods are capable of reproducing large scale facies continuity that is present in training images. Therefore, there is a need for methods that cure the above and other deficiencies of conventional MPS and object-based methodologies.